[E1452] More invasive refactoring.
 - Renamed usages of team 'member' to 'participant' to be more consistent.
 - Re-ordered and re-organized code so that it flows more logically as it
   is read.
 - Refactored some logic control statements so that they are easier to read
   (replacing !(<logic>) with unless, etc.)

Signed-off-by: Spenser James <sjames3@ncsu.edu>